Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x+5y &= -1 \\ 2x+9y &= 3\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $2x = -9y+3$ Divide both sides by $2$ to isolate $x$ $x = {-\dfrac{9}{2}y + \dfrac{3}{2}}$ Substitute this expression for $x$ in the first equation. $2({-\dfrac{9}{2}y + \dfrac{3}{2}}) + 5y = -1$ $-9y + 3 + 5y = -1$ Simplify by combining terms, then solve for $y$ $-4y + 3 = -1$ $-4y = -4$ $y = 1$ Substitute $1$ for $y$ in the top equation. $2x+5( 1) = -1$ $2x+5 = -1$ $2x = -6$ $x = -3$ The solution is $\enspace x = -3, \enspace y = 1$.